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In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…
In this article, we present a new type of fixed point for single valed mapping in a $G$-complete $G$-metric space.
We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained…
In this paper, inspired by the concept of generalized weakly contractive mappings in metric spaces, we introduce C-Class function and fixed point theory for weakly contractive in the setting of rectangular $b$-metric spaces and established…
Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
This paper introduces a new type of simulation function within the framework of $b$-metric spaces, leading to the derivation of fixed-point results in this general setting. We explore the theoretical implications of these results and…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
This paper introduces a novel generalization of the classical concept of $S$-metric spaces, referred to as composed $S$-metric spaces. By incorporating a composed function, we impose more general conditions on the triangle inequality,…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are…
We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.
In this paper, we introduce round and sleek topological spaces and study their properties.
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…
In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can…